\begin{tikzpicture}[>=Stealth, scale=0.4,
    every node/.style={fill=white, inner sep=1pt},
]
    \draw [->] (-8, 0) -- (8, 0) node[below=0.2em] {$x$} coordinate(x axis);
    \draw [->] (0, -8) -- (0, 8) node[left=0.2em]  {$y$} coordinate(y axis);
    \draw (0, 0) node [above left=0.3em] {\small $O$};
    \foreach \x in {1, ..., 6} {
        \draw (\x, 0) -- (\x, 0.2) node [above=0.2em] {\small $\x$};
    }
    \foreach \y in {-1, ..., -6} {
        \draw (0.2, \y) -- (0, \y) node [left=0.2em] {\small $\y$};
    }

    \draw[domain=0.9:6.5,   samples=50] plot (\x, {-6/\x});
    \draw[domain=-0.9:-6.5, samples=50] plot (\x, {-6/\x});
    \draw (3.5, -5)  node {$y = -\dfrac{6}{x}$};

    \foreach \x in {1, ..., 6} {
        \coordinate (a) at (\x, -6/\x);
        \draw [fill=black] (a) circle(0.1);
        \draw [dashed] (a |- x axis) -- (a) -- (a -| y axis);
    }
\end{tikzpicture}

